Chapter 7
COMPUTATION OF RATES AND OTHER MEASURES
Population bases
The rates shown in this report were computed on the basis of population
statistics prepared by the U.S. Bureau of the Census. Rates for 1940, 1950,
1960, 1970, and 1980 are based on the population enumerated as of
April 1 in the censuses of those years. Rates for all other years are based
on the estimated midyear (July 1) population for the respective years. Birth
rates for the United States, individual States, and metropolitan areas are
based on the total resident populations of the respective areas. Except as
noted these populations exclude the Armed Forces abroad but include the
Armed Forces stationed in each area.
The resident population of the birth- and death-registration States for
1900-32 and for the United States for 1900-89 is shown in table 4-1. In
addition, the population including Armed Forces abroad is shown for the
United States. Table B shows the sources for these populations.
Population estimates for 1981-89--The population of the United States
by age, race, and sex for 1989 is shown in table 4-2. The population for
each State is shown in table 4-3 and the monthly population figures were
published in Current Population Reports, Series P-25, Number 1067.
Comparable data for the U.S. population by age, race, and sex and for the
State populations for 1981-88, were shown, respectively, in tables 4-2 and
4-3 of Vital Statistics of the United States, volume I, for those years.
Comparable monthly population data for 1981-88 were shown in Current Pop-
ulation Reports, Series P-25, Numbers 931, 949, 961, 980, and 1001, 1021,
1023, and 1045. Data by race are consistent with the modified 1980
populations by race.
Populations for 1980-The population of the United States by age, race,
and sex, and the population for each State are shown in tables 4-2 and 4-3 of
Vital Statistics of the United States, 1980, volume I. The figures by race
have been modified as described below. Monthly population figures were
published in Current Population Reports, Series P-25, Number 899.
The racial counts in the 1980 census are affected by changes in racial
reporting practices, particularly by the Hispanic population, and in coding
and classifying racial groups in the 1980 census. One particular change has
created a major inconsistency between the 1980 census data and historical
data series, including censuses and vital statistics. About 40 percent of
the Hispanic population counted in 1980, over 5.8 million persons, did not
mark one of the specified races listed on the census questionnaire but
marked the "Other" category. In the 1980 census, coding procedures were
modified for persons who marked "Other" race and wrote in a national origin
destination of a Latin American country or a specific Hispanic origin group
in response to the racial question. These persons remained in the "Other"
racial category in 1980 census data; in previous censuses and in vital
statistics such responses were almost always coded into the "White" category.
To maintain comparability, the "Other" racial category in the 1980
census was reallocated to be consistent with previous procedures. Persons
who marked the "Other" racial category and reported any Spanish origin on the
Spanish origin question (5,840,648 persons) were distributed to white and
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Table B. Sources for resident population and population including Armed
Forces abroad: Birth-and death-registration States, 1900-1932, and United
States, 1900-1989.
-----------------------------------------------------------------------------
Year | Source
--------------|--------------------------------------------------------------
1989----------| U.S. Bureau of the Census, Current Population Reports,
| Series P-25, No. 1057, Mar. 1990.
1988----------| U.S. Bureau of the Census, Current Population Reports,
| Series P-25, No. 1045, Jan. 1990.
1986-87-------| U.S. Bureau of the Census, Current Population Reports,
| Series P-25, No. 1022, Mar. 1988.
1985----------| U.S. Bureau of the Census, Current Population Reports,
| Series P-25, No. 1000, Feb. 1987.
1984----------| U.S. Bureau of the Census, Current Population Reports,
| Series P-25, No. 985, Apr. 1986.
1983----------| U.S. Bureau of the Census, Current Population Reports,
| Series P-25, No. 965, Mar. 1985.
1982----------| U.S. Bureau of the Census, Current Population Reports,
| Series P-25, No. 949, May 1984.
1981----------| U.S. Bureau of the Census, Current Population Reports,
| Series P-25, No. 929, May 1983.
1980----------| U.S. Bureau of the Census, U.S. Census of Population:
| 1980, Number of Inhabitants, PC80-1-A1, United States
| Summary,1983.
1971-79-------| U.S. Bureau of the Census, Current Population Reports,
| Series P-25, No. 917, July 1982.
1970----------| U.S. Bureau of the Census, U.S. Census of Population:
| 1970, Number of Inhabitants, Final Report PC(1)-A1,
| United States Summary, 1971.
1961-69-------| U.S. Bureau of the Census, Current Population Reports,
| Series P-25, No. 519, Apr. 1974.
1960----------| U.S. Bureau of the Census, U.S. Census of Population:
| 1960, Number of Inhabitants, PC(1)-A1, United States
| Summary, 1964.
1951-59-------| U.S. Bureau of the Census, Current Population Reports,
| Series P-25, No. 310, June 30, 1965
1940-50-------| U.S. Bureau of the Census, Current Population Reports,
| Series P-25. No. 499, May 1973
1930-39-------| U.S. Bureau of the Census, Current Population Reports,
| Series P-25, No. 499, May 1973, and National Office of
| Vital Statistics, Vital Statistics Rates in the United
| States, 1900-1940, 1947
1920-29-------| National Office of Vital Statistics, Vital Statistics
| Rates in the United States, 1900-1940, 1947
1917-19-------| Same as for 1930-39.
1900-16_______| Same as for 1920-29.
______________|___________________________________________________________________
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black races in proportion to the distribution of persons of Hispanic origin
who reported their race to be white or black. This was done for each age-sex
group.
As a result of this procedure, 5,705,155 persons were added to the white
population and 135,493 persons to the black population. Persons who marked
the "Other" racial category and reported that they were not of Spanish
origin (916,338 persons) were distributed as follows: 20 percent in each
age-sex group were added to the "Asian and Pacific Islander" category
(183,268 persons) and 80 percent were added to the "White" category
(733,070 persons). The count of American Indians, Eskimos, and Aleuts was
not affected by these procedures. Unpublished tabulation of these modified
census counts were obtained from the U.S. Bureau of the Census and used to
compute the 1980 rates for this report, except for tables 1-15 through 1-22.
Population estimates for 1971-79--Birth rates for 1971-79 (except
those for cohorts of women in tables 1-15 through 1-22) have been revised,
based on revised population estimates that are consistent with the 1980
census levels, and thus may differ from rates published in volumes of Vital
Statistics of the United States for these years. The 1980 census counted
approximately 5.5 million more persons than had earlier been estimated for
April 1, 1980 (14). The revised estimates for the United States by age,
race, and sex were published by the U.S. Bureau of the Census in Current
Population Reports, Series P-25, Number 917. Population estimates by month
are based on data published in Current Population Reports, Series P-25,
Number 899. Unpublished revised estimates for States were obtained from the
U.S. Bureau of the Census.
Population estimates for 1961-69--Birth rates in this volume for
1961-69 (except for those shown in tables 1-5 and 1-6) are based on revised
estimates of the population and thus may differ slightly from rates
published before 1976. The revised estimates used in computing these rates
were published in Current Population Reports, Series P-25, Number 519. The
rates shown in tables 1-5 and 1-6 for 1961-64 are based on revised
estimates of the population published in Current Population Reports, Series
P-25, Numbers 321 and 324 and may differ slightly from rates published in
those years.
Population estimates for 1951-59--Final intercensal estimates of the
population by age, race, and sex and total population by State for 1951-59
are shown in tables 4-4 and 4-5 of volume I, Vital Statistics of the United
States, 1966. Beginning with 1963 these final estimates have been used to
compute birth rates for 1951-59 in all issues of Vital Statistics of the
United States.
Net census undercounts and overcounts
The U.S. Bureau of the Census has conducted extensive research to
evaluate the coverage of the U.S. population (including undercount,
overcount, and misstatement of age, race, and sex) in the last five
decennial censuses--1950, 1960, 1970, and 1980. These studies provide
estimates of the national population that was not enumerated or
overenumerated in the respective censuses, by age, race, and sex (15-17).
The report for 1980 (unpublished data from the Bureau of the Census)
includes estimates of net underenumeration and overenumeration for age, sex,
and racial subgroups of the national population, modified for race
consistency with previous population counts as described in the section
cmpnat89.doc - Page 3
"Populations for 1980."
These studies indicate that there is differential coverage in the
censuses among the population subgroups; that is, some age, race, and sex
groups are more completely enumerated than others. To the extent that these
estimates of overcounts or undercounts are valid, that they are substantial,
and that they vary among subgroups and geographic areas, census miscounts
can have consequences for vital statistics measures (15). However, the
effects of undercounts in the census are reduced to the extent that there is
underregistration of births. If these two factors are of equal magnitude,
rates based on unadjusted populations are more accurate than those based on
adjusted populations because the births have not been adjusted for
underregistration.
The impact of net census miscounts on vital statistics measures
includes the effects on levels of the rates and effects on differentials
among groups.
If adjustments were made for persons who were not counted in the census
of population, the size of the denominators would generally increase and the
rates would be smaller than without an adjustment. Adjusted rates for 1980
can be computed by multiplying the reported rates by ratios of the 1980
census-level population adjusted for the estimated net census miscounts,
which are shown in table C. A ratio of less than 1.0 indicates a net census
undercount and would result in a corresponding decrease in the rate. A ratio
in excess of 1.0 indicates a net census overcount and would result in a
corresponding increase in the rate.
Enumeration of white females in the childbearing ages was at least 99
percent complete for all ages. Among women of races other than white, the
undercount ranged up to 4 percent. Generally, females in the childbearing
ages were more completely enumerated than males for similar race-age groups.
If vital statistics measures were calculated with adjustments for net
census miscounts for each of these subgroups, the resulting rates would have
been differentially changed from their original levels; that is, rates for
those groups with the greatest estimated overcounts or undercounts would
show the greatest relative changes due to these adjustments. Thus the
racial differential in fertility between the white and the "All other"
population can be affected by such adjustments.
Cohort fertility tables
The various fertility measures shown for cohorts of women in tables
1-15 through 1-22 are computed from births adjusted for underregistration
and population estimates corrected for underenumeration and misstatement of
age. The data shown in this volume are not consistent with data published
in annual reports before 1974. These data use revised population estimates
prepared by the U.S. Bureau of the Census and have been expanded to include
data for the two major racial groups. Heuser has prepared a detailed
description of the methods used in deriving these measures as well as more
detailed data for earlier years (18).
Parity distribution--The percent distribution of women by parity
(number of children ever born alive to mother) shown in tables 1-17 and 1-21
is derived from cumulative birth rates by order of birth, which are shown in
tables 1-16 and 1-20. The percent of zero-parity women is found by
subtracting the cumulative first birth rate from 1,000 and dividing by 10.
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Table C. Ratio of census-level resident population to resident population
adjusted for estimated net census undercount by age,race,and sex:
April 1, 1980
______________________________________________________________________________
| All races | White |
|_______________________________|_______________________________|
Age | Both | Male | Female | Both | Male | Female |
| Sexes | | | Sexes | | |
_____________|_________|__________|__________|__________|__________|________ |
All ages | 0.9862 | 0.9763 | 0.9958 | 0.9916 | 0.9839 | 0.9990 |
10-14 years | 0.9978 | 0.9982 | 0.9974 | 1.0003 | 1.0008 | 0.9998 |
15-19 years | 1.0011 | 0.9983 | 1.0034 | 1.0003 | 0.9976 | 1.0003 |
20-24 years | 0.9834 | 0.9706 | 0.9965 | 0.9879 | 0.9769 | 0.9993 |
25-29 years | 0.9742 | 0.9581 | 0.9908 | 0.9799 | 0.9673 | 0.9929 |
30-34 years | 0.9850 | 0.9683 | 1.0020 | 0.9905 | 0.9778 | 1.0036 |
35-39 years | 0.9776 | 0.9597 | 0.9955 | 0.9860 | 0.9730 | 0.9991 |
40-44 years | 0.9743 | 0.9549 | 0.9937 | 0.9849 | 0.9706 | 0.9992 |
45-49 years | 0.9734 | 0.9538 | 0.9926 | 0.9828 | 0.9690 | 0.9967 |
50-54 years | ... | 0.9638 | ... | ... | 0.9755 | ... |
55 years | | | | | | |
and older | ... | 0.9865 | ... | ... | 0.9875 | ... |
15-44 years | ... | ... | 0.9973 | ... | ... | 0.9995 |
15-54 years | ... | 0.9683 | ... | ... | 0.9770 | ... |
_____________|_________|__________|__________|__________|__________|_________|
______________________________________________________________________________
| All other |
| ______________________________________________________________|
| Total | Black |
|_______________________________|_______________________________|
Age | Both | Male | Female | Both | Male | Female |
| Sexes | | | Sexes | | |
_____________|_________|__________|__________|_________|__________|__________|
All ages | 0.9543 | 0.9309 | 0.9765 | 0.9392 | 0.9103 | 0.9669 |
10-14 years | 0.9858 | 0.9858 | 0.9859 | 0.9808 | 0.9807 | 0.9816 |
15-19 years | 1.0051 | 1.0052 | 1.0055 | 0.9980 | 0.9958 | 1.0001 |
20-24 years | 0.9590 | 0.9354 | 0.9819 | 0.9390 | 0.9076 | 0.9696 |
25-29 years | 0.9422 | 0.9040 | 0.9786 | 0.9168 | 0.8695 | 0.9628 |
30-34 years | 0.9519 | 0.9081 | 0.9931 | 0.9197 | 0.8638 | 0.9735 |
35-39 years | 0.9248 | 0.8743 | 0.9736 | 0.8968 | 0.8322 | 0.9588 |
40-44 years | 0.9107 | 0.8576 | 0.9614 | 0.8782 | 0.8135 | 0.9401 |
45-49 years | 0.9124 | 0.8544 | 0.9669 | 0.8833 | 0.8139 | 0.9497 |
50-54 years | ... | 0.8759 | ... | ... | 0.8413 | ... |
55 years | | | | | | |
and older | ... | 0.9779 | ... | ... | 0.9578 | ... |
15-44 years | ... | ... | 0.9848 | ... | ... | 0.9712 |
15-54 years | ... | 0.9157 | ... | ... | 0.8843 | ... |
_____________|_________|__________|__________|_________|__________|__________|
SOURCE: U.S. Bureau of the Census: Estimates of the population of the
United States, by age, sex, and race: 1980 to 1985. Current Population
Reports, Series P-25, No. 985. Washington, U.S. Government Printing
Office, Apr. 1986.
cmpnat89.doc - Page 5
The proportions of women at parities one through six are found from the
following formula:
(cum. rate, order N)-(cum. rate, order N+1)
Percent at N parity = -------------------------------------------
10
The percent of women at seventh higher parities is found by dividing
the cumulative rate for seventh-order births by 10.
Birth probabilities--Shown in tables 1-18 and 1-22, birth probabilities
indicate the likelihood that a woman of a certain parity and age at the
beginning of the year will have a child during the year. Birth probabilities
differ from central birth rates in that the denominator for birth
probabilities is specific for parity as well as for age.
Age-sex-adjusted birth rates
The age-sex-adjusted birth rates shown in table 1-4 are computed by the
direct method. The age distribution of women aged 10-49 years as enumerated
in 1940 and the total population of the United States for that year are used
as the standard populations. The birth rates by age of mother and race that
are used to compute these adjusted rates are shown in table 1-9. The
age-sex-adjusted birth rates show differences in the level of fertility
independent of differences in the age and sex composition of the population.
It is important not to confuse these adjusted rates with the crude rates
shown in other tables.
Total fertility rate
The total fertility rate is the sum of the birth rates by age of mother
(in 5-year age groups) multiplied by 5. It is an age-adjusted rate because
it is based on the assumption that there are the same number of women in
each age group. In table 1-9 the rate of 2,014 in 1989, for example, means
that if a hypothetical group of 1,000 women were to have the same birth
rates in each age group that were observed in the actual childbearing
population in 1989, they would have a total of 2,014 children by the time
they reached the end of the reproductive period (taken here to be age 50
years), assuming that all of the women survived to that age.
Intrinsic vital rates
The intrinsic vital rates shown in table 1-6 are calculated from a
stable population. A stable population is that hypothetical population,
closed to external migration, that would become fixed in age-sex structure
after repeated applications of a constant set of age-sex specific birth and
death rates. For the mathematical derivation of intrinsic vital rates, see
pages 4-13 and 4-14 in the Technical Appendix of volume I, Vital Statistics
of the United States, 1962. The technique of calculating intrinsic vital
rates is described by Barclay(19).
cmpnat89.doc - Page 6
Seasonal adjustment of rates
The seasonally adjusted birth and fertility rates shown in table 1-8
are computed from the X-11 variant of Census Method II (20). This method of
seasonal adjustment used since 1964 differs slightly from the U.S. Bureau of
Labor Statistics (BLS) Seasonal Factor Method, which was used for Vital
Statistics of the United States, 1964. The fundamental technique is the same
in that it is an adaptation of the ratio-to-moving-average method. Before
1964 the method of seasonal adjustment was based on the X-9 variant and
other variants of Census Method II. A comparison of the Census Method II
with the BLS Seasonal Factor Method shows the differences in the seasonal
patterns of births to be negligible.
Computation of percents, medians, and means
Percent distributions, medians, and means are computed using only
events for which the characteristic is reported. The "Not stated" category
is subtracted from the total before computation of these measures.
The asterisk (*) indicates that the numerator and/or denominator number
is less than 20.
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